In this project, I wanted to look and see if 3-point percentages had increased over the years, as it seems volume certainly has. So I randomly selected 15 players who have played at least 8 seasons, have a 15-minute/game average for their careers and average at least 7.0 points per game. Random.org was used to generate the team to pull from, then again to select a player.

Just a quick look at player shooting per season

Red shows field goal attempts and green shows field goals made

A look into overall shooting using the formula below finds no significance between the interaction of season, player and field goal attempts on percentages

## [1] 0.01729683
## fg_percent ~ season * player * fga

3-Point Shooting for all players over their seasons. We see a shooting volume increase, which help foment the hypothesis that the league might be shooting better from distance

Red = 3-pointers attempted, green = 3-pointers made, and the blue line indicates 3-point %. For percentages 1 on the graph would = 100% shooting

Now for each player

Red = 3-pointers missed, green = 3-pointers made, and the blue line indicates 3-point %

3-Point percentages for players

A better look at percentages

0.1 is 10% and 0.5 Is 50% shooting

Analyzing interaction of season and player on 3-point percentages. Significance and residual

## x3p_percent ~ season * player
## [1] 0.07207535

Predictions of the above formala

Predictions in red and 3-point percentage is green

Now, analyzing interaction of season, player, and 3-pointers attempted on 3-point percentages. Significance and residual

## [1] 0.05862911
## 
## Call:
## glm(formula = x3p_percent ~ season * player * x3pa, data = Full_Data)
## 
## Deviance Residuals: 
##       Min         1Q     Median         3Q        Max  
## -0.243148  -0.025831   0.001345   0.024033   0.248441  
## 
## Coefficients:
##                                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                           78.48329   20.62749   3.805 0.000218 ***
## season                                -0.03888    0.01023  -3.799 0.000222 ***
## playerBradley Beal                   -96.30801  116.69335  -0.825 0.410708    
## playerChris Paul                    -101.03458   38.05986  -2.655 0.008932 ** 
## playerDamian Lillard                 -67.81600  105.67169  -0.642 0.522158    
## playerDanilo Gallinari               -40.83713   52.87266  -0.772 0.441299    
## playerDeMar DeRozan                  -86.27952   28.36859  -3.041 0.002849 ** 
## playerGordon Hayward                  80.64878   40.92651   1.971 0.050897 .  
## playerIsh Smith                      -68.48368   30.24495  -2.264 0.025212 *  
## playerJeff Teague                   -104.35748   32.94051  -3.168 0.001913 ** 
## playerJonas Valanciunas             -347.11025   61.27221  -5.665 9.02e-08 ***
## playerKemba Walker                  -102.98089   97.96102  -1.051 0.295097    
## playerNikola Vucevic                 -92.46990   41.60846  -2.222 0.027986 *  
## playerRajon Rondo                    -95.96076   29.12070  -3.295 0.001267 ** 
## playerRicky Rubio                    -49.42765  101.79332  -0.486 0.628090    
## playerTobias Harris                  -92.97690   51.25092  -1.814 0.071961 .  
## x3pa                                 381.98977  201.13501   1.899 0.059758 .  
## season:playerBradley Beal              0.04790    0.05791   0.827 0.409661    
## season:playerChris Paul                0.05026    0.01890   2.659 0.008813 ** 
## season:playerDamian Lillard            0.03374    0.05236   0.644 0.520479    
## season:playerDanilo Gallinari          0.02037    0.02628   0.775 0.439719    
## season:playerDeMar DeRozan             0.04285    0.01408   3.044 0.002830 ** 
## season:playerGordon Hayward           -0.04003    0.02032  -1.970 0.050927 .  
## season:playerIsh Smith                 0.03402    0.01502   2.265 0.025140 *  
## season:playerJeff Teague               0.05189    0.01636   3.172 0.001887 ** 
## season:playerJonas Valanciunas         0.17232    0.03041   5.666 9.00e-08 ***
## season:playerKemba Walker              0.05116    0.04868   1.051 0.295238    
## season:playerNikola Vucevic            0.04594    0.02066   2.224 0.027897 *  
## season:playerRajon Rondo               0.04771    0.01447   3.298 0.001258 ** 
## season:playerRicky Rubio               0.02460    0.05053   0.487 0.627210    
## season:playerTobias Harris             0.04622    0.02546   1.816 0.071739 .  
## season:x3pa                           -0.18911    0.09962  -1.898 0.059874 .  
## playerBradley Beal:x3pa             -374.95488  202.10655  -1.855 0.065828 .  
## playerChris Paul:x3pa               -375.57450  201.39750  -1.865 0.064458 .  
## playerDamian Lillard:x3pa           -382.47189  201.75974  -1.896 0.060222 .  
## playerDanilo Gallinari:x3pa         -390.07932  201.33067  -1.938 0.054852 .  
## playerDeMar DeRozan:x3pa            -379.10819  201.71751  -1.879 0.062428 .  
## playerGordon Hayward:x3pa           -421.16052  201.40265  -2.091 0.038462 *  
## playerIsh Smith:x3pa                -376.04543  201.86243  -1.863 0.064736 .  
## playerJeff Teague:x3pa              -374.93642  201.60815  -1.860 0.065184 .  
## playerJonas Valanciunas:x3pa        -129.59884  214.97269  -0.603 0.547651    
## playerKemba Walker:x3pa             -376.76926  201.52225  -1.870 0.063787 .  
## playerNikola Vucevic:x3pa           -374.56593  201.69887  -1.857 0.065566 .  
## playerRajon Rondo:x3pa              -385.34820  201.51045  -1.912 0.058038 .  
## playerRicky Rubio:x3pa              -392.64531  204.83140  -1.917 0.057442 .  
## playerTobias Harris:x3pa            -382.29009  201.45610  -1.898 0.059962 .  
## season:playerBradley Beal:x3pa         0.18562    0.10010   1.854 0.065959 .  
## season:playerChris Paul:x3pa           0.18593    0.09975   1.864 0.064589 .  
## season:playerDamian Lillard:x3pa       0.18935    0.09993   1.895 0.060331 .  
## season:playerDanilo Gallinari:x3pa     0.19313    0.09972   1.937 0.054949 .  
## season:playerDeMar DeRozan:x3pa        0.18770    0.09991   1.879 0.062526 .  
## season:playerGordon Hayward:x3pa       0.20858    0.09975   2.091 0.038483 *  
## season:playerIsh Smith:x3pa            0.18619    0.09998   1.862 0.064826 .  
## season:playerJeff Teague:x3pa          0.18561    0.09986   1.859 0.065318 .  
## season:playerJonas Valanciunas:x3pa    0.06389    0.10649   0.600 0.549554    
## season:playerKemba Walker:x3pa         0.18653    0.09981   1.869 0.063905 .  
## season:playerNikola Vucevic:x3pa       0.18544    0.09990   1.856 0.065677 .  
## season:playerRajon Rondo:x3pa          0.19078    0.09981   1.911 0.058148 .  
## season:playerRicky Rubio:x3pa          0.19440    0.10146   1.916 0.057544 .  
## season:playerTobias Harris:x3pa        0.18927    0.09978   1.897 0.060070 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.005023852)
## 
##     Null deviance: 1.8386  on 189  degrees of freedom
## Residual deviance: 0.6531  on 130  degrees of freedom
##   (4 observations deleted due to missingness)
## AIC: -416.68
## 
## Number of Fisher Scoring iterations: 2
This is the mod that displays great significance of our categories’ correlation to 3-point shooting and the mod shows good residuals compared to other categorical interactions. ‘Players’ shows a lot of significance, as well as certain seasons they played.

3-Point % vs season

Added trend line. We see mostly either positive or flat slopes, a couple negative. This looks like it supports the idea that 3-point percentages may be increasing through the seasons.

3-point percentages and attempts per season

Red = 3-pointers attempted and blue shows the percentages for each season
We definitely see volume increases. But maybe it just became mathematically better to shoot more threes as long as percentages didn’t dip, but we do see some more slightly positive increases. Perhaps it was purely mathematical to green light the shooting of more 3-pointers, and players naturally practiced them more and became better at them.

Predictions using the above interacting formula

Added predictions = red and green shows 3-point % for each season

Predicting into the next 4 future seasons

We see some strong looking predictions, but be mindful that these are showing small overall percentage changes, but they give us an obvious trend to spot.

Interactions of player and minutes per game + season on 3-point %

## x3p_percent ~ player * mp + season
## [1] 0.06984445

This mod shows us significance

Minutes and 3-point % vs Seasons

Given a player shoots good or bad, I’d expect a gain or reduction in minutes.

We see minutes do have an effect 3-point %, but only for certain players. It appears that a consistently decent 3-point % might a good factor into what’s keeping the player playing more minutes. A guy like Andre Drummond, is a traditional big and earns minutes by other methods, but limits spearding the floor like a lot of teams like to do these days.

Interactions of player, position, and season on 3-point %

Another aspect to consider would be that of position. Primary ball-handlers, typicaly the guard, might see different kind of shots then say a center, who will likely only take open threes. But a center’s body type has typically, in the past, not seen them as finesse players with long distant shooting skills.
## x3p_percent ~ player * pos * season
## [1] 0.07164746
What could be done in the future is collect mean data from many players at each position and compare those values since there isn’t a big enough pool to draw from within this data-set.